Numerade

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1. A bank is not obligated to honor a check if the drawer’s account does not contain enough money to pay the amount of the check. Forged or altered checks Insufficient funds Stale checks Stop-payment orders Postdated checks

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(1 point) Use the properties of logarithms to rewrite ln $$ \frac{2x(x+6)}{x+10} $$ as a sum/difference of logarithms. NOTE: If you get a weird error when you try to preview your answer, it is probably because you haven't fully expanded your answer. Your final answer should have no multiplications or divisions. ln $$ \frac{2x(x+6)}{x+10} $$

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a) Determine the closed-loop transfer function T(s) = Y(s)/R(s), assume Td(s) = 0. b) Determine the sensitivity of the transfer function with respect to small changes in K1 and K. c) Determine the steady-state error for a step input R(s) = 1/s. d) Determine the steady-state error due to a disturbance Td(s) = 1/s (assume R(s) = 0). e) Calculate the response y(t) for a unit step input when K=K2 =1 and K1 = 10, assume Td(s) = 0.

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Given the examples below, which is most likely to be a monopoly? local fast-food restaurant local electricity distributor local bathroom fixtures shop local television broadcaster

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The use of irony, derision, or wit to expose folly or wickedness is known as Multiple Choice metaphor. contrast. dialect. satire.

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When CPI inflation is greater than GDP deflator inflation it must be because:

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6. Let T be the linear operator on $M_{n \times n}(\mathbb{R})$ defined by $T(A) = A^T$. (a) Show that $\pm 1$ are the only eigenvalues of T. (b) Describe the eigenvectors corresponding to each eigenvalue of T. (c) Find an ordered basis $\beta$ for $M_{2 \times 2}(\mathbb{R})$ such that $[T]_\beta$ is a diagonal matrix. (d) Find an ordered basis $\beta$ for $M_{n \times n}(\mathbb{R})$ such that $[T]_\beta$ is a diagonal matrix for $n > 2$.

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1. Let G = D12 = \langle a, b : a^6 = b^2 = 1, b^{-1}ab = a^{-1} \rangle. Define the matrices A, B, C, D over \mathbb{C} by $A = \begin{pmatrix} e^{i\frac{\pi}{3}} & 0\\ 0 & e^{-i\frac{\pi}{3}} \end{pmatrix}$, $B = \begin{pmatrix} 0 & 1\\ 1 & 0 \end{pmatrix}$, $C = \begin{pmatrix} \frac{1}{2} & \frac{\sqrt{3}}{2}\\ -\frac{\sqrt{3}}{2} & \frac{1}{2} \end{pmatrix}$, $D = \begin{pmatrix} 1 & 0\\ 0 & -1 \end{pmatrix}$. (a) Prove that each of the functions $\rho_k : G \to GL(2, \mathbb{C})$ given by $\rho_1 : a^r b^s \mapsto A^r B^s$, $\rho_2 : a^r b^s \mapsto A^3 r (-B)^s$, $\rho_3 : a^r b^s \mapsto (-A)^r B^s$, $\rho_4 : a^r b^s \mapsto C^r D^s$, where $0 \le r \le 5$ and $0 \le s \le 1$, is a representation of G. (b) Which of these representations are faithful? Which are equivalent? (c) How does G acts on $\mathbb{C}^2$ by $\rho_k$ for $1 \le k \le 4$?

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Please help me with questions a to e with steps. Thanks. Suppose that there are 200 students interested in using the Recreational Sports Facility (RSF). The quality of the RSF is denoted by G. The nicer the facility is (higher G), the more each user enjoys it. The total cost of building the RSF is rising in quality: TC(G) = 10G + 15G^2, where "c" is a constant that represents a fixed cost of building the RSF. The 200 students have identical preferences. Initially, we will assume that there is no congestion, and TBi(G) = 5G. a) Solve for G^*, the optimal quality of the RSF. b) True or false: the optimal level of the public good is different if c = 10,000 as it will be if c = 20,000. (Hint: the Samuelson condition holds for an "interior solution", where G > 0, but it is always possible to choose G = 0, which will be optimal if the total project is not worth building. We did not discuss this in class, so I wanted to make the point here.) c) Now, suppose that, as in the real RSF, congestion is a problem and that the more users using the facility, the lower the benefits for each user. Specifically, suppose now that the total benefit for a user allowed into the RSF is TBi(G) = 5G - N/4. The cost function is the same. Note: Actually, in the results that you will get below, if N > 0 then the public good should not be built because the total benefits will be too small under the congestion benefit function. Please ignore this. Or, you can assume that N is a large negative number, so that the total costs are low enough to justify building the good. Ignore any potential effects of beta on the decision of how much of the public good to provide. Intuitively, do you think that this congestion should increase or lower the new optimal value (label this G*)? Explain why in 1-2 sentences. (I recommend that you make reference to the Samuelson condition in your answer.) d) Find G* and N*, which is the optimal number of users. (Was your prediction about the size of G* compared to G* correct?) e) At N* and G*, what is the total benefit per user? What is the lost utility from congestion caused by the last user (i.e., take the derivative of total social benefits at the optimum with respect to N)? (What is true about these two values)?

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Numerical Part: (100 Marks) Question 7: (5) A synchronous motor rated 4000 hp (3000 kW), 200 rpm, 6.9 kV, 60 Hz, 80% power factor designed to drive an ore crusher. The brushless exciter (alternator/rectifier) is mounted on the overhung shaft and rated 50kW, 250 V. Calculate the number of salient poles on the rotor of the synchronous motor. Question 8: (5) A 4000 hp (3000 kW), 6600 V, 60 Hz, 200 rpm synchronous motor operates at full load at a leading power factor of 0.8. If the synchronous reactance is, calculate the following: a. The apparent power of the motor, per phase b. The ac line current c. The value and phase of the Excitation voltage, d. Draw the phasor diagram e. Determine the torque angle,

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consuelo j.